let and be two events such that the occurrence of implies the occurrence of , but not vice-versa. Then, the correct relation between the probabilities and is:

Explanation: To solve this, we must interpret the logical relationship between the two events using Set Theory and Probability axioms. 1. Understanding the relationship: "The occurrence of implies the occurrence of " means that whenever event happens, event must also happen. In terms of sets, this implies that is a subset of : "Not vice-versa" means that can occur without occurring. Therefore, is a proper subset of ( ). 2. Relating to Probability: For any two events where , the probability of must be less than or equal to the probability of : Since the problem explicitly states that the implication does not work "vice-versa," it implies there is a non-zero probability that occurs while does not. Thus, the probability of must be strictly greater than the probability of :

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TEZPUR 2025 — Mathematics PYQ

TEZPUR | Mathematics | 2025

let $A$ and $B$ be two events such that the occurrence of $A$ implies the occurrence of $B$ , but not vice-versa. Then, the correct relation between the probabilities $P (A)$ and $P (B)$ is:

Choose the correct answer: